$\begin{align}  & \frac{2-2\sqrt{2}+\sqrt{5}}{2-2\sqrt{2}-\sqrt{5}}=\frac{2-(2\sqrt{2}-\sqrt{5})}{2-(2\sqrt{2}+\sqrt{5)}} \\ & \frac{2-(2\sqrt{2}-\sqrt{5})}{2-(2\sqrt{2}+\sqrt{5)}}=\frac{2-(2\sqrt{2}-\sqrt{5})}{2-(2\sqrt{2}+\sqrt{5)}}\times \frac{2+(2\sqrt{2}+\sqrt{5)}}{2+(2\sqrt{2}+\sqrt{5})} \\ & \frac{2-(2\sqrt{2}-\sqrt{5})}{2-(2\sqrt{2}+\sqrt{5)}}=\frac{4+2(2\sqrt{2}+\sqrt{5})-2(2\sqrt{2}-\sqrt{5})+\left[ -(2\sqrt{2}-\sqrt{5})(2\sqrt{2}+\sqrt{5}) \right]}{4-{{\left[ (2\sqrt{2}+\sqrt{5}) \right]}^{2}}} \\ & \frac{2-(2\sqrt{2}-\sqrt{5})}{2-(2\sqrt{2}+\sqrt{5)}}=\frac{4+4\sqrt{2}+2\sqrt{5}-4\sqrt{2}+2\sqrt{5}+\left[ -(8-5) \right]}{4-\left[ 8+5+4\sqrt{10} \right]} \\ & \frac{2-(2\sqrt{2}-\sqrt{5})}{2-(2\sqrt{2}+\sqrt{5)}}=\frac{4+4\sqrt{5}-3}{4-\left[ 13+4\sqrt{10} \right]}=\frac{1+4\sqrt{5}}{4\sqrt{10}-9} \\ & \frac{2-(2\sqrt{2}-\sqrt{5})}{2-(2\sqrt{2}+\sqrt{5)}}=\frac{(1+4\sqrt{5})(4\sqrt{10}+9)}{\left[ 4\sqrt{10}-9 \right]\left[ 4\sqrt{10}+9 \right]} \\ & \frac{2-(2\sqrt{2}-\sqrt{5})}{2-(2\sqrt{2}+\sqrt{5)}}=\frac{4\sqrt{10}+9+80\sqrt{2}+36\sqrt{5}}{160-81} \\ & \frac{2-(2\sqrt{2}-\sqrt{5})}{2-(2\sqrt{2}+\sqrt{5)}}=\frac{9+80\sqrt{2}+36\sqrt{5}+4\sqrt{10}}{79} \\\end{align}$